Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1846 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 1846 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#11763663 | C2 | direct (N × H) |
| 11. #11763663 | C22 | direct (N × H) |
| 15. C2×#10587632 | C4 | semidirect |
| 17. C22×C4⋊Dic17 | C4 | semidirect |
| 20. C23×Q8×C17 | C4 | semidirect |
| 28. C22×Q8×C17 | C2×C4 | semidirect |
| 43. #10587632 | C2×C4 | semidirect |
| 48. C2×C4⋊Dic17 | C2×C4 | semidirect |
| 70. C2×Q8×C17 | C22×C4 | semidirect |
| 95. C4⋊Dic17 | C22×C4 | semidirect |
| 142. C22×C17 | #328 | semidirect |
| 164. C23×Q8 | #595 | semidirect |
| 180. C2×C17 | C2×#328 | semidirect |
| 190. C22×Q8 | C2×#595 | semidirect |
| 221. C17 | C22×#328 | semidirect |
| 232. C2×Q8 | C22×#595 | semidirect |
| 314. C22 | #11763663 | direct (N × H) |
| 329. C2 | C2×#11763663 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587543 | 2 |
| C22×(C2×#595)⋊C4 | 2 |
| C2×#11763663 | 2 |
| C22×#10587632 | 2 |
| C22×#328 | 17 |